华东师范大学学报(自然科学版) ›› 2005, Vol. 2005 ›› Issue (3): 17-23.

• 数学 统计学 • 上一篇    下一篇

非对称几何控制图在质量控制中的应用

濮晓龙, 姚红   

  1. 华东师范大学统计系, 上海200062
  • 收稿日期:2003-12-16 修回日期:2004-01-06 出版日期:2005-08-25 发布日期:2005-08-25
  • 通讯作者: 濮晓龙

Application of Asymmetric Geometric Charts for High Quality Process (Chinese)

PU Xiao-long, YAO Hong   

  1. Department of Statistics, East China Normal University, Shanghai 200062, China
  • Received:2003-12-16 Revised:2004-01-06 Online:2005-08-25 Published:2005-08-25
  • Contact: PU Xiao-long

摘要： 在质量控制过程中, 对于检测不合格率p的变化,特别是p较小时, 基于几何分布的控制图( g-type chart)比基于二项分布的控制图(p-chart或np-chart)能更有效地检测并报警.但几何控制图经常会出现下限LCL为零的情况,而由于检测产品数的非负性, 当LCL为零时,几何控制图就不会出现报警,因而此时对检测p的增加几乎是没有效果的.该文提出非对称控制图的思想, 解决了零下限的问题,而且非零下限有效地提高了控制图p增加时的检测能力,其受控平均运行长度ARL和对称 (传统) 的控制图几乎相同.得到的数据可以在实际应用中确定控制限.

关键词: 对称控制限, 非对称控制限, ARL, OC曲线, 对称控制限, 非对称控制限, ARL, OC曲线

Abstract:

The control chart based on the geometric distribution(g-type chart )has been shown to be competitive with p or np chart for monitoring the proportion,especially for applications in high quality manufacturing environments.However when the cases with LCL=0 occur, plotting values beneath the LCL is impossible given the non-negative nature of units such type of lower control limit has no ability to detect rate increase. In fact,situation with a LCL is not uncommon. In this paper we propose the g-type chart with asymmetric control limits.It is found that with the nonzero LCL,the power to detect rate increase has much improved and the power to detect rate decrease is nearly fixed, while the in-control average run length(ARL)is the almost the same as the conventional(symmetric) control chart. In practice,the quantitative results of the paper can be used to determined the control limits.

Key words: asymmetric control limits, ARL, OC curve, symmetric control limits, asymmetric control limits, ARL, OC curve

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